6758 • The Journal of , June 22, 2016 • 36(25):6758–6770

Systems/Circuits Using Diffusion Tractography to Predict Cortical Connection Strength and Distance: A Quantitative Comparison with Tracers in the Monkey

X Chad J. Donahue,1 XStamatios N. Sotiropoulos,2 XSaad Jbabdi,2 XMoises Hernandez-Fernandez,2 Timothy E. Behrens,2 XTim B. Dyrby,3,4 XTimothy Coalson,1 Henry Kennedy,5 XKenneth Knoblauch,5 David C. Van Essen,1* and Matthew F. Glasser1* 1Department of Neuroscience, Washington University School of Medicine, St. Louis, Missouri 63110, 2Oxford Centre for Functional MRI of the , University of Oxford, Oxford, United Kingdom OX3 9DU, 3Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital, Hvidovre, Denmark 2650, 4Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark 2800, and 5Stem-cell and Brain Research Institute, Bron, France 69500

Tractography based on diffusion MRI offers the promise of characterizing many aspects of long-distance connectivity in the brain, but requires quantitative validation to assess its strengths and limitations. Here, we evaluate tractography’s ability to estimate the presence and strength of connections between areas of macaque neocortex by comparing its results with published data from retrograde tracer injections. Probabilistic tractography was performed on high-quality postmortem diffusion imaging scans from two Old World monkey . Tractography connection weights were estimated using a fractional scaling method based on normalized streamline density. We foundacorrelationbetweenlog-transformedtractographyandtracerconnectionweightsofrϭ0.59,twicethatreportedinarecentstudy on the macaque. Using a novel method to estimate interareal connection lengths from tractography streamlines, we regressed out the distance dependence of connection strength and found that the correlation between tractography and tracers remains positive, albeit substantially reduced. Altogether, these observations provide a valuable, data-driven perspective on both the strengths and limitations of tractography for analyzing interareal corticocortical connectivity in nonhuman primates and a framework for assessing future tractog- raphy methodological refinements objectively. Key words: ; connectivity; diffusion tractography; macaque; ; retrograde tracing

Significance Statement Tractography based on diffusion MRI has great potential for a variety of applications, including estimation of comprehensive maps of neural connections in the brain (“”). Here, we describe methods to assess quantitatively tractography’s performance in detecting interareal cortical connections and estimating connection strength by comparing it against published results using neuroanatomical tracers. We found the correlation of tractography’s estimated connection strengths versus tracer to be twice that of a previous study. Using a novel method for calculating interareal cortical distances, we show that tractography- based estimates of connection strength have useful predictive power beyond just interareal separation. By freely sharing these methods and datasets, we provide a valuable resource for future studies in cortical connectomics.

Introduction anatomy and circuitry. These include characterizing trajectories Tractography based on diffusion MRI (dMRI) is used widely to of major (WM) fiber bundles (Catani and Thiebaut obtain several complementary types of information about brain de Schotten, 2008; Glasser and Rilling, 2008) and subdividing (parcellating) gray matter (GM) regions based on tractography-

Received Feb. 8, 2016; revised May 10, 2016; accepted May 14, 2016. Author contributions: C.J.D., D.C.V.E., and M.F.G. designed research; C.J.D., T.E.B., T.C., H.K., K.K., D.C.V.E., and theFrenchNationalResearchAgency(GrantsANR-11-BSV4-501,ANR-14-CE13-0033,LabExCORTEXANR-11-LABX- M.F.G. performed research; S.N.S., S.J., M.H.-F., T.E.B., T.E.B.D., H.K., T.C., and M.F.G. contributed unpublished 0042, and Universite´ de Lyon ANR-11-IDEX-0007 to H.K.), and the National Institutes of Health (Grant reagents/analytictools;C.J.D.,S.N.S.,S.J.,D.C.V.E.,andM.F.G.analyzeddata;C.J.D.,S.N.S.,S.J.,T.E.B.,T.E.B.D.,H.K., P01AG026423) and the Yerkes National Primate Research Center (Office of Research Infrastructure Programs Grant K.K., T.C., D.C.V.E., and M.F.G. wrote the paper. OD P51OD11132) for the scans used for the macaque atlas, and to T. Preuss and J. Rilling. We thank Drs. R. Palmour This work was supported by the National Institutes of Health (Grant R01 MH 60974 to D.C.V.E. and Grant F30 and M. Ptito and the Behavioral Science Foundation of St-Kitts (West Indies) for providing the Vervet monkey MH097312 to M.F.G.), the Engineering and Physical Sciences Research Council (Grant EP/L023067/1 to S.N.S.), and specimens (PM2) for ex vivo imaging. Donahue et al. • Connection Strength and Distance with Tractography J. Neurosci., June 22, 2016 • 36(25):6758–6770 • 6759 derived connectivity profiles (“connectional contrast”; Behrens two areas relative to the number of streamlines extrinsic to those et al., 2003; Johansen-Berg et al., 2004; Rushworth et al., 2006; areas. To investigate a known tractography-path-length depen- Beckmann et al., 2009; Mars et al., 2011). Here, we focus on using dency (Basser et al., 2000; Liptrot et al., 2014), we compared two tractography to estimate the presence and weight (“strength”) of tractography seeding strategies for their impact on overall trac- long-distance connections between GM regions. This involves tography performance. analysis of “parcellated connectomes”; that is, estimating con- Tracer-based connection weights decline approximately ex- nectivity between brain subdivisions (parcels) in humans or non- ponentially with interareal separation (Ercsey-Ravasz et al., human primates (NHPs) (Sporns et al., 2005; Harriger et al., 2013). Using a new tractography-based method for estimating 2012; Li et al., 2013; Reid et al., 2016; van den Heuvel et al., 2015). interareal separation, we show that tractography remains mod- Tractography is an indirect method for inferring connectivity estly informative in predicting connection presence and weight and various methodological confounds introduce noise and/or after regressing out an exponential relationship with path length. bias (Jbabdi and Johansen-Berg, 2011; Jones et al., 2013; Van These limitations of tractography likely reflect major anatomical Essen et al., 2014). Validation studies are needed that compare features, such as the organization of WM bundles subjacent to against “ground truth” data from anatomical tracer studies in sulcal fundi (Reveley et al., 2015; see Discussion). laboratory animals. Previous studies in NHPs demonstrate both successes and limitations of tractography for assessing pathway Materials and Methods trajectories (Jbabdi et al., 2015; Kno¨sche et al., 2015) and detect- ing the presence of long-distance interareal connections (Jbabdi Macaque retrograde tracer data. Markov et al. (2014) quantified intra- hemispheric interareal connectivity in the macaque cortex using retro- et al., 2013; Thomas et al., 2014; Azadbakht et al., 2015; Reveley et grade tracers and reported weighted connectivity of 29 input injection al., 2015). It is equally important to examine the accuracy of areas in an atlas of 91 cortical areas; that is, a 29 ϫ 91 weighted and tractography-estimated connection weights given the high directed connectivity matrix. This 91-area parcellation, originally gener- density of the cortical graph (Markov et al., 2014) and the fact ated from a histologically based surface reconstruction of an individual that connection weights are fundamental to understanding cor- macaque left hemisphere (M132), was registered to the macaque “F99” tical organization (Ercsey-Ravasz et al., 2013). A recent system- atlas using a landmark-constrained registration algorithm in Caret atic comparison in the mouse (Calabrese et al., 2015) revealed a (Markov et al., 2014). We used the MSM-Sulc algorithm (Robinson et al., correlation coefficient of r ϭ 0.46 between log-transformed, 2014) to register the F99 atlas to a new population average macaque high-resolution postmortem tractography data and quantitative Macaca mulatta atlas (“Yerkes19,” as described below). Figure 1A shows tracer-based connectivity data (Oh et al., 2014). In contrast, van the M132 parcellation displayed on the inflated macaque Yerkes19 atlas ϭ left hemisphere. The locations of cortical area relative to gyral and sulcal den Heuvel et al. (2015) reported much lower correlations (r landmarks on the atlas surface are similar, but not identical, to those in 0.25–0.31) when comparing in vivo macaque tractography with the original M132 surface reconstructed from histological sections. Fig- two published tracer-based connectivity analyses. Given method- ure 1B shows the locations of reported injection sites (Markov et al., ological limitations in data acquisition (e.g., coarse spatial reso- 2014) mapped to the atlas surface. lution, low angular resolution diffusion scans) and analysis (e.g., The weight of the projection from each injected area to any given a coarse cortical parcellation; see Discussion) in the latter study, source area was defined as the FLNe, the fraction of labeled neurons in a this may not reflect the upper bound for tractography perfor- source area relative to the total number of labeled neurons extrinsic to the mance in primates. injected area (Markov et al., 2011, 2014). The connection weights deter- mined by this method span five orders of magnitude and are distributed In the present study, we used high-resolution postmortem diffu- ϫ sion imaging combined with complex fiber orientation modeling in a lognormal fashion. A 29 91 area connectivity matrix (“parcellated ”) was generated using the areal parcellation and incorpo- and probabilistic tractography to evaluate systematically tractogra- rating into the data matrix the tracer connectivity values reported by phy performance in estimating the existence and the weights of area- Markov et al. (2014) in logarithmic (log10) units. Results were repre- to-area connectivity throughout cerebral cortex in Old World sented using the Connectivity Informatics Technology Initiative data monkeys. As an approximation of ground truth, we used published format (http://www.nitrc.org/projects/cifti/), which enables interactive quantitative data generated using retrograde tracers injected into 29 visualization of connectivity maps and connectivity matrices in Connec- cortical areas in the macaque using a 91-area atlas parcellation tome Workbench (http://humanconnectome.org/software/). (Markov et al., 2014). This constitutes the most comprehensive For the tracer injections, each injection provided information restricted to weighted tracer-based connectivity matrix currently available for the inputs to a particular area. Therefore, a complete description of both inputs and outputs is available only for the 29 ϫ 29 edge-complete subgraph NHPs. Tractography results were generated from diffusion imaging ϫ of postmortem brains from Old World monkeys (macaque and of the larger 29 91 connectivity matrix. Directionality was removed by calculating the arithmetic mean of each pair of anterograde and retrograde vervet) that have very similar cortical convolutions and, likely, con- connection weights. We refer to the 29 ϫ 29 retrograde tracer (RT) parcel- nectivity patterns. lated connectivity matrix as RT29ϫ29, or the RT matrix for short. Retrograde tracer interareal connection weights range over dMRI data acquisition. We analyzed dMRI scans from both the left and five orders of magnitude when quantified as the fraction of la- right hemispheres of two postmortem monkey brains (PM1 and PM2), beled neurons (FLNe) in each area relative to the total number of the second of which was analyzed for two separate scans: (PM2A and labeled neurons extrinsic to the injected area (Markov et al., 2011, PM2B). PM1 involved diffusion-weighted MRI of an immersion-fixed 2014). We used an analogous “fractional scaling” metric for trac- brain from an adult male, macaque, M. fascicularis (D’Arceuil et al., tography based on the fraction of streamlines (FSe) connecting 2007). The postmortem brain was infused with a gadolinium contrast agent that enables acquisition using short TR (D’Arceuil et al., 2007). Scans were acquired using a 3D multishot, spin-echo sequence on a 4.7 T Bruker scanner with the following scan parameters: TR ϭ 250 ms; TE ϭ The authors declare no competing financial interests. ϭ ϫ ϫ *D.C.V.E. and M.F.G. are co-senior authors. 31.7 ms; matrix size 256 128 128; isotropic 0.43 mm voxels. Correspondence should be addressed to David C. Van Essen, Washington University School of Medicine, 660 S. Diffusion weighting was applied in 120 uniformly distributed directions 2 Euclid Avenue, St. Louis, MO 63110. E-mail: [email protected]. with b ϭ 8000 s/mm . Total imaging time was ϳ27 h. DOI:10.1523/JNEUROSCI.0493-16.2016 PM2A and PM2B were acquired from a perfusion-fixed brain of a Copyright © 2016 the authors 0270-6474/16/366759-13$15.00/0 healthy adult 32-month male vervet (Chlorocebus sabaeus) brain. The 6760 • J. Neurosci., June 22, 2016 • 36(25):6758–6770 Donahue et al. • Connection Strength and Distance with Tractography animal was obtained from the Behavioral Science Foundation, St. Kitts, Data were mapped from individual experimental hemispheres to the Ye- and was socially housed in enriched environments. The experimental rkes19 atlas using surface-based registration, as described below. Visua- protocol was reviewed and approved by the Institutional Review Board of lization used Connectome Workbench software (http://www.humanco the Behavioral Science Foundation acting under the auspices of the Ca- nnectome.org/software/connectome-workbench.html). nadian Council on Animal Care. Preparation of the postmortem brain dMRI preprocessing. Because the diffusion data were not echo-planar and the collection of data on a preclinical 4.7 T Agilent MR scanner (at imaging (EPI) based and were from fixed tissue, many typical prepro- the Danish Research Centre for Magnetic Resonance) involved the ex cessing steps (motion correction, eddy current correction, and b0 inho- vivo imaging setup described previously (Dyrby et al., 2011, 2014). The mogeneity correction) were not required. Cortical surface models were scan session started with a Ͼ4 h diffusion-weighted image (DWI) derived directly from the high-resolution (Յ0.5 mm) diffusion data us- dummy scan ensuring reduction of short-term instabilities introduced in ing steps that yielded analogs of the T1w and T2w images needed for the acquisition of the DWI datasets. In two separate scan sessions, the acceptable FreeSurfer segmentation. First, FSL’s bedpostX algorithm (Jb- PM2A and PM2B were collected using a 2D pulsed-gradient-spin-echo abdi et al., 2012) was run using modeling of three fibers and the aniso- sequence with single-line readout. Scan parameters for PM2A and PM2B tropic volume fractions from each fiber were summed across fibers. This were as follows: TR ϭ [5100, 6500] ms; TE ϭ [45, 35] ms; NEX ϭ [1, 2] produces an image that highlights anisotropic WM and avoids decreased (averaged offline); matrix size ϭ 128 ϫ 256; whole brain coverage of axial intensity in regions containing well behaved crossing fibers. A T1w-like slices with isotropic 0.5 mm voxels. The b-value was [4000, 7500] s/mm 2, image having contrast similar to a conventional T1-weighted image was 3bϭ 0 s/mm 2 acquired in [61, 128] uniformly and noncollinear direc- generated by taking the fourth root of the sum of volume fractions image. tions using the scheme files available from the Camino tool kit (Cook et A T2w-like image having contrast similar to conventional T2-weighted ϭ al., 2006). Total imaging times for PM2A and PM2B were ϳ20 and was obtained from the mean of the b 0 images. These two high- 68.5 h, respectively. resolution T1w-like and T2w-like images were fed into the PreFree- The Yerkes19 macaque atlas. To enable accurate comparisons across Surfer, FreeSurferNHP, and PostFreeSurfer pipelines described above. results obtained in different individuals and between left and right hemi- For the high-resolution tractography analysis, the 32k mesh was used spheres, tracer and MRI data were registered to a group-average “Ye- (0.8 mm average vertex spacing). rkes19” macaque surface-based atlas (Van Essen et al., 2012a). This atlas Fiber orientation modeling was performed using a model-based de- was based on structural MRI scans (T1w and T2w, 0.5 mm isotropic) of convolution approach (Jbabdi et al., 2012) to estimate up to three cross- 19 adult macaques acquired at Yerkes Primate Research Center at Emory. ing fibers per voxel. We used the RubiX framework (Sotiropoulos et al., Each brain was processed using the minimal preprocessing pipelines 2013) to further regularize these orientations. RubiX jointly estimates developed for the (HCP) (Glasser et al., orientations in neighborhoods of voxels. To apply RubiX on a single 2013) to extract cortical surfaces and subcortical volumes from the struc- resolution of data, the data were downsampled by half (e.g., from 0.5 to tural MRI scans and align individual scans to the template. 1 mm) and RubiX was applied to both resolutions (i.e., the original and downsampled data). When used in this way, some soft spatial constraints The HCP pipelines (developed for human MRI data) were adapted to are imposed directly on the parameter space and the model acts as an work with monkey MRI. For the in vivo scans used to generate the atlas, edge-preserving spatial filter. Pilot analyses indicated that such an ap- the PreFreeSurfer pipeline aligned T1w and T2w volumes to native an- proach slightly increased precision of the orientation estimates and the terior commissure–posterior commissure space, allowing brain extrac- incidence of WM voxels modeled by three crossing fiber bundles in re- tion, cross-modal registration, bias field correction, and FMRIB Software gions where we expected complex fiber structure. It was therefore pre- Library (FSL) analysis (Smith et al., 2004) of nonlinear volume registra- ferred in this study to the more standard voxelwise estimation approach. tion to atlas space (as is done in the human HCP pipelines). Aside from Importantly, none of the results depends heavily on or changes signifi- using macaque volume templates, this only required adjustment of the cantly due to this spatial filtering choice. brain size parameter to 80 mm. A customized pipeline (FreeSurferNHP) Probabilistic tractography. Tractography was performed in native vol- adapted from the FreeSurfer pipeline included the following NHP- ume space using the WM/GM boundary surface registered to the same specific changes: (1) brain extraction and initial intensity nonuniformity 32k mesh used for the Yerkes19 atlas. Probabilistic tractography was correction were done outside of FreeSurfer, in this case using the Pre- performed using FSL’s probtrackx (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/ ء ͱ FreeSurfer brain extraction and T1w T2w bias field correction FDT/UserGuide; Behrens et al., 2007) using a [1/4] voxel step size con- methods, and (2) the data were converted into a “fake” 1 mm isotropic 3 strained by a 90° threshold for maximal curvature (angle difference) 256 space [in “RAS” (right anterior superior) orientation] to conform between successive steps choosing the fiber orientation with least angular to FreeSurfer’s requirements without interpolation (Fischl, 2012). Free- deviation from the previous tractography step. Recent versions of the Surfer 12 parameter affine and nonlinear registrations used a species- tractography toolbox (probtrackx2 in FSL version 5.0 and higher) sup- specific volume template, as did subcortical segmentation. The standard port tracking using surfaces and volumes simultaneously (Sotiropoulos HCP FreeSurfer pipeline was then used up to the point of surface regis- et al., 2013). As a general inclusion criterion, streamlines were counted if tration, when a species-specific surface template was used. FreeSurfer they intersected the surface mesh representing the WM/GM boundary at stages after pial surface generation (e.g., cortical parcellation) were not a minimum of two locations. Such intersections are indicated at the level done. Finally, the volume and surface data were transformed from the of tiles of the surface tessellation equivalent to small planar patches FreeSurfer “fake” 1 mm RAS space back into the right posterior inferior parallel to the local WM/GM boundary. To avoid artifactual loops, input space (0.5 mm rigidly aligned to the macaque volume template) streamlines were terminated if they crossed the pial surface, traversed and cortical thickness was recomputed. The PostFreeSurfer pipeline was subcortical GM or a ventricle, or revisited a previously traversed voxel. run using multimodal surface matching (MSM) surface registration Tractography was conducted separately for the left and right cerebral (Robinson et al., 2014) using FreeSurfer’s “sulc” measure of cortical hemispheres to reduce computational time and storage requirements shape to drive the alignment (MSM-Sulc). This pipeline generates a high- and because the retrograde tracer data were available only for intrahemi- resolution (“164k”) surface mesh (ϳ164,000 vertices per hemisphere). spheric connectivity. The resulting data included (cortical GM) ϫ (cor- This was resampled to form two lower resolution meshes (32k and 10k) tical GM) “dense connectomes” (cortical GM) ϫ (WM) ϫ (fiber used for subsequent analyses. Interhemispheric alignment between the orientation) “trajectory files” (to enable visualization of fiber trajecto- left and right hemispheres was based on landmark-based alignment anal- ries), and (cortical GM) ϫ (cortical GM) “streamline average distance ogous to that performed on the macaque F99 atlas surfaces (Van Essen et matrices” (to enable computation of distances between areas along the al., 2012a) using 45 geographically corresponding landmark contours in tractography streamlines). In this study, tractography-derived connec- each hemisphere. For the two postmortem monkeys analyzed in this tivity was computed using two seeding strategies: unidirectional sur- study, identical steps were performed for the structural preprocessing face-to-surface and bidirectional voxel-to-surface (see Fig. 1C,D), each with the exception of the creation of T1w- and T2w-like images described yielding a dense diffusion tractography matrix (dDT1 and dDT3, in the next section. respectively). Donahue et al. • Connection Strength and Distance with Tractography J. Neurosci., June 22, 2016 • 36(25):6758–6770 • 6761

WM/GM surface to WM/GM surface (dDT1). dDT1 was generated with relatively few are needed to achieve statistical sensitivity (Ambrosen et al., the probtrackx algorithm by seeding from every vertex on the WM/GM 2013; Liptrot et al., 2014). For each voxel, random locations were gener- boundary surface. For each vertex, random locations were generated ated within a sphere with a diameter equal to the voxel edge length and within a sphere with a diameter equal to the voxel edge length and cen- centered on the voxel’s center. Streamlines were seeded from these loca- tered on the vertex’s coordinates. The voxel containing this random tions. This resulted in a GM-by-GM connectivity matrix in which the location was chosen as the origin of a streamline, the initial orientation of number of streamlines was again used as a surrogate for connection which was drawn from the underlying fiber distribution (based on the weight. randfib and fibst options in probtrackx). Propagation through other Evaluating biases in cortical connectivity. One component of the gyral voxels was as described above. A streamline that crossed a second tile of bias for tractography (see Introduction) is attributable to the geometry of the WM/GM surface was assigned to that tile’s nearest surface vertex. A cortical convolutions insofar as the wedge-like folding of cortex implies streamline connecting a pair of vertices, beginning and ending at the that a unit surface area of the WM/GM interface is associated with a WM/GM boundary surface, was considered a candidate anatomical con- different cortical volume and therefore predicts higher streamline den- nection and the streamline count at both vertices was incremented. The sity in gyral crowns and lower streamline density in sulcal fundi. This seeding process was repeated 5000 times per seed vertex (regardless of geometrically predicted bias was estimated using the ratio of cortical GM how many streamlines were successful), yielding a connectivity matrix volume in a given wedge to the surface area of the WM under this wedge (“dense connectome”) of cortical GM to GM structural connectivity, in (Van Essen et al., 2014). The observed tractography bias was calculated which the number of streamlines between each pair of vertices was used by averaging streamline density across “source” vertices in dDT1/3. To as a surrogate for connection weight (see below). compare the predicted and actual biases directly, each vertex value was The strategy of seeding at vertices along the WM/GM boundary sur- divided by the mean value at zero curvature Ϯ 0.025, thus normalizing face and stopping streamlines when they encountered the WM/GM the values of each. Values were converted to a logarithmic scale for easier boundary at a different location was designed to estimate long-distance comparison and visualization. Note that the appearance of the above corticocortical connectivity comprehensively within the WM proper, patterns would be less easy to predict for tractography algorithms that given known anatomical and tractography constraints. We did not at- count streamlines on the cortical surface using voxels rather than using tempt to analyze trajectories within the cortical GM, for example, to/ surface tiles and vertices as performed here. This is due to the lower from the specific cellular layers in which originate and terminate spatial specificity and a greater partial volume effect, as described above. (or to a surrogate single layer such as the cortical midthickness, as was Parcellated tractography connectomes. Dense tractography matrices done by Reveley et al., 2015). This is because using tractography to were parcellated in two ways using command-line tools in the Connec- assess trajectories within GM introduces confounds that, in our tome Workbench. Our primary analyses were based on an “injection- view, compound rather than ameliorate the challenges of tractography site-to-area” method, in which connectivity values were weighted in the through WM. One reason is that the dominant diffusion orientation vicinity of each of the 29 reported tracer injection sites (see Fig. 1B) using within deep layers of GM is often tangential, especially in and near sulcal a circular Gaussian distribution on the cortical surface centered at the fundi (in our data and also in Fig. 1D,H of Reveley et al., 2015; see also injection site, thereby generating an intermediate “(source-injection- Fig. 7 in Dyrby et al., 2011); this presumably reflects a strong tangential zone) ϫ (target-vertex)” connectivity matrix. The full width at half max- plexus of dendritic as well as axonal arborizations in the deep layers. imum used was 1.9 mm, based on the estimated spread of retrograde Accordingly, tracking streamlines through deep cortical layers will fre- tracer uptake reported by Markov et al. (2011). Averaging across vertices quently lead to misalignment between streamline start/stop locations in in each parcel resulted in an injection-site-to-area 29 ϫ 91 parcellated GM and the point at which streamlines cross into WM. This contrasts connectivity matrix. We also implemented an “area-to-area” method in with anatomical observations that axons of cortical projection neurons which connectivity values were averaged across parcel vertices in each of generally descend radially until they reach WM and input axons tend to the 91 cortical areas in the M132 parcellation to generate an intermediate ascend radially before arborizing in their target layers (Rockland and “(source-area) ϫ (target-vertex)” connectivity matrix (i.e., a 91 ϫ 32k Virga, 1989, 1990; Coogan and Burkhalter, 1993). Another consideration matrix). Identical averaging in the other direction resulted in a 91 ϫ 91 is that ascending and descending axons often take sharp turns (i.e., with parcellated connectivity matrix. a radius of curvature much smaller than a dMRI voxel) in the WM near From both of these parcellated tractography connection matrices, the WM/GM boundary, particularly in and near the fundus of a sulcus the 29 ϫ 29 area edge-complete subgraph from the tracer study was (Figs. 16.12, 16.13 of Van Essen et al., 2014; Figs. 4, 5 of Reveley et al., extracted, and used for all analyses comparing tractography and tracer

2015). In such regions, it is very difficult for current tractography algo- data. We will refer to these as the pDT129ϫ29 and pDT329ϫ29 matrices rithms to track streamlines associated with a high radius of curvature at (pDT1 and pDT3 for short), respectively. or near the WM/GM boundary. Instead, our approach initiates stream- Tractography-estimated interareal path lengths. Tractography-based lines associated with a seed vertex based on the modeled fiber orientation estimates of interareal pathway length were computed using probtrackx, distribution in the nearest WM voxel. When such a voxel occupies a which outputs a dense distance matrix of mean streamline length be- predominantly tangential fiber plexus in superficial WM under a sulcus tween connected vertices. This dense matrix was then parcellated using a (Reveley et al., 2015), it is expected that many streamlines will not accu- weighted version of the “area-to-area” method described previously, in rately represent actual trajectories of axons crossing the nearby WM/GM which the number of streamlines encountering each vertex was used to boundary. Such cases will contribute to erroneous connectivity esti- weight within-parcel average distances. This weighting makes the esti- mates, but represent a fair test of tractography performance and limita- mate a mean length of all the streamlines that reached the area, instead of tions given current methods. being a mean of the lengths associated with each vertex within the area by WM to WM/GM surface (dDT3). dDT3 was designed to mitigate a emphasizing vertices having a larger number of streamlines. probabilistic distance bias inherent to tractography, in which streamlines Normalizing connection weights. Comparisons between tracer and trac- for short pathways are more likely to be identified than those for long tography data were facilitated by normalizing both measures of connec- pathways (Li et al., 2012; Liptrot et al., 2014). To reduce this bias, we tion weights. As noted above, FLNe provides a quantitative and objective initiated tractography from every WM voxel enclosed in the WM surface measure of tracer connection weights. For tractography, we estimated and seeded from fiber orientations in the seed voxel according to their connection weights based on the number of streamlines between any pair anisotropic volume fraction. We tracked in both directions along the of surface vertices. In particular, we implemented a method of FSe to chosen seed orientation and counted connections that intersected the describe connection weights in tractography-derived matrices. WM surface once in each direction. We seeded 100 times per seed voxel, Because the dDT1 connectivity matrix is by nature asymmetric, sym- reasoning that, because there are many more WM voxels than surface metry could not be assumed in computing fractionally scaled values. For vertices at the WM boundary, the resulting computational time and this reason, it becomes important to define the index notation of con- average connection density should match that of dDT1. Our analysis nectivity values: DTi,j denotes the number of streamlines initiated at area should not be especially sensitive to the number of streamlines because index i and terminated at area index j. Generally, the FSe value for a 6762 • J. Neurosci., June 22, 2016 • 36(25):6758–6770 Donahue et al. • Connection Strength and Distance with Tractography

Figure1. Markovetal.(2014)macaquecorticalparcellationmappedtotheinflatedlefthemisphereoftheMacaqueYerkes19atlasanddiffusiontractographyseedingstrategies.A,The91-area parcellationusedforbothretrogradetracerandtractographyanalyses.B,The29areasassociatedwithcorticalinjectionsitesareas,withinjectionlocations(blackspheres)reportedbyMarkovetal. (2014) projected to the cortical surface. C, dDT1, surface-to-surface tractography seeding strategy. D, dDT3, dual voxel-to-surface tractography seeding strategy. Full data are available at https://balsa.wustl.edu/RP92.

pathway originating in some area A and terminating in some area B is Evaluating tractography detection performance. The receiver operating defined as the ratio of the number of streamlines originating at A and characteristic (ROC), sensitivity and specificity were used to measure the terminating at B to the total number of streamlines that either origi- capacity of tractography to predict the existence of a connection using nate at A or terminate at B while excluding streamlines that represent self tracer connection weights as an estimate of “ground truth.” Both corre- (within-area) connections. Therefore, for a connectivity matrix of N ϫ N lation and detection performance are necessary in interpreting tra- areas, DT, we computed the fractionally scaled value of FSe(DT) for each ctography’s ability to estimate connectivity because both acceptable area pair as follows: correlation and reliable detection are needed to consider results neuro- biologically interpretable. DTi, j FSe͑DT ͒ ϭ , where x  i & y  j Relationship between tractography performance and path length. Con- i, j ͸N ϩ ͸N nections were allocated by their length into bins covering a range of 10 xϭ1DTi, x yϭ1DTy, j mm. In each bin, the median value of tracer and tractography connec- In this study, fractional scaling was performed after averaging within tions was computed. either areas or injection site domains, thus using 91 ϫ 91 and 29 ϫ 91 parcellated connectome weight matrices. This makes all parcellated trac- tography matrices comparable to one another, as well as to the FLNe Results connection weight metric used to describe tracers. Within-area (area-to- Folding-related biases self) connections were not considered in this analysis and their Cortical folding introduces a geometric bias in which the amount connection weights were set to the minimum threshold value for both of cortical GM per unit area of the WM/GM surface is elevated in tracer and tractography datasets. Symmetrization via arithmetic mean a gyral crown and reduced in a sulcal fundus relative to that in a ϩ DTi, j DTj,i flat sulcal bank (Van Essen et al., 2014). If the number of axons i.e., ͩ ͪ was performed after computing the fractionally 2 entering and leaving the cortex depends on cortical volume, then scaled connection weights. Because connection weight values span many there should be a gyral bias in axonal density crossing the orders of magnitude, most analyses were performed in log-space using WM/GM boundary. This in turn predicts a geometrically based log connection weights. Averaging of connection weights across hemi- 10 gyral bias in tractography streamline density, which may be ex- spheres was performed for corresponding vertices of the dense connec- acerbated by the observation that the dominant fiber bundles in tome (dDT1/3) based on interhemispheric alignment of the Yerkes19 atlas mesh. diffusion imaging voxels within gyral blades tend to be oriented Correlation while excluding tractography and tracer weights. Correla- along the axis pointing toward gyral crowns (Van Essen et al., tion coefficients were used to determine the degree to which pDT1/3 2014). To examine this issue, we used two distinct tractography reflect those described by RT. The effect size ␩2 was computed to quantify seeding methods to estimate connectivity matrices for dense the variance shared between pDT1/3 and RT. Correlation coefficients (vertex-based, dDT) and for parcellated (area-based, pDT) were first computed for the full pDT1/3 and RT matrices. Subsequently, representations. The seeding strategies (Fig. 1C,D), identified the strongest interareal connection in the tracer matrix was removed as either dDT1 (unidirectional surface-to-surface) or dDT3 (bi- from both the tractography matrix being assessed and the RT matrix. The directional white-matter-voxel-to-surface), yielded strikingly correlation coefficient of the resulting matrices was then computed and different patterns of overall streamline density. Figure 2 com- the process was repeated until all connections had been removed. Be- pares these patterns with that predicted by the aforementioned cause the aim of this analysis was to quantify tractography’s ability to characterize connection weights reliably, only nonzero weighted connec- geometric cortical folding bias (Van Essen et al., 2014). The fold- tions were considered (i.e., all false positives/negatives and true negatives ing pattern for macaque postmortem 1 (PM1; Fig. 2A) predicts a were excluded from the analysis, effectively thresholding for connection geometric bias (Fig. 2B) in which the density of axonal connec- strengths greater than zero). The impact of these false positives/negatives tions should be elevated in gyral crowns and reduced in sulcal is described by the subsequent detection analyses. fundi relative to flat sulcal banks by a magnitude that is approx- Donahue et al. • Connection Strength and Distance with Tractography J. Neurosci., June 22, 2016 • 36(25):6758–6770 • 6763

Parcellated connectivity analyses The dense tractography matrices dDT1 and dDT3 were converted to initial hemisphere- specific parcellated matrices pDT1 and pDT3, respectively, using the 91-area corti- cal parcellation generated by Markov et al. (2014) and mapped to the Yerkes19 group average surface-based atlas. Tractography- based parcellated connectivity matrices (“parcellated connectomes”) were highly correlated between left and right hemi- spheres of individual brains (PM1: r ϭ 0.86, PM2A: r ϭ 0.92, PM2B: r ϭ 0.93). There- fore, the tractography results reported here were averaged across hemispheres and dis- played after registration to the left hemi- sphere of the atlas surface. Fractional scaling was then implemented to generate the final pDT1 and pDT3 connectivity matrices. Figure 3A shows the tracer-based par- cellated connectivity map (connection weights) averaged across multiple injec- tions in foveal V1 (Markov et al., 2011, 2014), revealing notably strong connec- tions with several extrastriate visual areas, including V2, V4, MT, and TEO. Also shown are pDT1 connectivity maps for monkey PM1 (Fig. 3B) using a seeding method restricted to the location of the tracer injection (injection-site-to-area or IS-A method; see Materials and Meth- ods). Visual inspection suggests that trac- tography examples exhibit patterns similar to those produced by tracers, though with some important differences. For example, area MT is more weakly con- nected with V1 according to tractography than tracer. The tractography maps also Figure 2. Geometry-predicted versus observed tractography streamline density biases for monkey PM1 normalized to the show consistent false positives in medial mean streamline density at flat regions (sulcal banks). A, Folding pattern. B, Geometric bias predicted via the ratio of cortical GM parietal, insular, and somatomotor re- volume to WM surface area. C, D, Observed tractography bias of dDT1/3 computed via average streamline density at each surface gions that are low to moderate in esti- vertex. Scale bars are in log2 units. Full data are available at https://balsa.wustl.edu/R7kj. mated weight. The false-positive medial pathways may reflect trajectories that run through the large bundle. In Figure 3C, the tracer injection in area F5 imately symmetric across gyral and sulcal regions and has a range reveals connectivity with 72 cortical areas, including all areas of twice that of the average connection density. The relative density frontal cortex and areas 2 and SII of parietal cortex. The pDT1 of observed tractography streamlines in dDT1 (Fig. 2C) shows map for PM1 (Fig. 3D) also shows connectivity with frontal re- modest regional differences that are not correlated with the gions and moderate connectivity with areas 2 and SII. Similar ϭϪ folding-predicted bias (r 0.08). In contrast, dDT3 (Fig. 2D) trends for both V1 and F5 connectivity were observed using exhibits streamline densities that exceed the prediction in many pDT3. ϭ regions (both gyral and sulcal), yet correlate with it modestly (r Retrograde tracers identify unidirectional pathways, whereas 0.36). Further inspection of these biases suggest that streamlines tractography is inherently bidirectional given the physical nature may be particularly underrepresented in sulcal regions and some- of the water diffusion signal. Our primary comparisons with trac- what overrepresented in gyral regions, consistent with observa- tography used the symmetrized 29 ϫ 29 subgraph of the full tions of Reveley et al. (2015); this contrasts with the relatively (29 ϫ 91) tracer matrix. As performance metrics, we report the unbiased distributions of retrogradely labeled neurons ob- Pearson correlation coefficient (r) to describe linear dependences served in tracer studies (Markov et al., 2011, 2014). Therefore, and ␩2 to indicate the proportion of associated variance (which the overall fidelity of estimates of axonal densities using func- would differ from r 2 if there were a nonlinear dependence). Sep- tions of the number of tractography streamlines will be af- arate connectivity matrices were computed using tracer injection fected by such biases. However, they should be ameliorated in sites as seeds (IS-A) or by a whole area-to-area method (A-A). a parcellated analysis to the degree that each cortical area The fractionally scaled pDT129ϫ29 IS-A matrices were reasonably spans a mixture of gyral and sulcal cortex. correlated with tracer (PM1: r ϭ 0.59, ␩2 ϭ 0.35; PM2A: r ϭ 0.60, 6764 • J. Neurosci., June 22, 2016 • 36(25):6758–6770 Donahue et al. • Connection Strength and Distance with Tractography

Figure 3. Tracer and tractography log-scale connection weights for area V1 (A, B) and F5 (C, D). Retrograde tracer connection weights were based on FLNe to each injected area from the full 91-area parcellation. Tractography brain postmortem 1 was FSe. Areas V1 and F5 are labeled in blue in A, B and C, D, respectively. Black spheres illustrate the corresponding tracer injection sites for each area. Full data are available at https://balsa.wustl.edu/R698 and https://balsa.wustl.edu/R1Xr.

␩2 ϭ 0.36 and PM2B: r ϭ 0.55, ␩2 ϭ 0.31), with all subject A-A 2a/2b, respectively). Figure 4A illustrates fractionally scaled PM1 cases showing similar correlation values (same value for PM1 connection weights plotted against tracer, with data points la- IS-A and A-A). The 29 ϫ 29 IS-A matrices were highly correlated beled according to their tractography-based interareal path across brains and scans (PM1/2A: r ϭ 0.89; P1/2B: r ϭ 0.85 and length. For high values of FLNe (tracer), the tractography weights PM2A/2B: r ϭ 0.94). (FSe) are slightly below the diagonal, indicating that tractography In the following, we report results for PM1 parcellated using tends to underestimate connection weights by a modest amount the IS-A method. PM1 was chosen to minimize species differ- for the most strongly connected pathways, which are generally ences (tracer and PM1 were both macaques; PM2 was a vervet); fairly short (Ͻ20 mm). For moderately and weakly connected the IS-A method was used to better emulate the focal nature of the anatomical pathways, the degree of correlation is less evident tracer injections. PM2A and PM2B, scanned with b values of 4000 visually. and 8000 s/mm 2, respectively, provide additional insight into Another measure of tractography’s performance examined how differences in scan parameters may affect tractography per- correlations while progressively removing connections from formance (see Supplemental Materials). strongest to weakest as reported by tracer. We analyzed only true Compared with absolute streamline densities, fractional scal- positives (connections detected by both tractography and tracer; ing and symmetrization improved tractography’s correlations n ϭ 309) to avoid penalizing tractography for binary detection both with tracer (from r ϭ 0.48 to r ϭ 0.59 and from ␩2 ϭ 0.23 to mistakes; that is, excluding false positives (n ϭ 76), false negatives ␩2 ϭ 0.35) and between pDT1 and pDT3 in the same animal (n ϭ 13), and true negatives (n ϭ 8). As shown in Figure 4B, the (correlation between the 91 ϫ 91 pDT1 and pDT3 matrices (log correlation with tracer for both pDT1 and pDT3 becomes weaker values, fractionally scaled) yielded r ϭ 0.95, 0.96, 0.97 for PM1/ as progressively more high-weight connections are excluded; Donahue et al. • Connection Strength and Distance with Tractography J. Neurosci., June 22, 2016 • 36(25):6758–6770 • 6765

Figure 4. Tracer versus tractography performance comparison. A, Scatterplot of RT vs tractography (pDT1) log-scale connection weights in case PM1. Data points are depicted according to their correspondingpathlengthbin(binwidthϭ20mm;excludedpathlengthsϾ80mm,nϭ10).Thesolidlinedenotestheleastabsoluteresidualsfittodataexcludingpointsalongeitheraxis(false negatives:nϭ13;falsepositives:nϭ76).Thedashedline( yϭx)isforreference.B,CorrelationbetweentractographyandtracerconnectivityweightincasePM1forpDT1andpDT3.Dottedlines represent second-order polynomial fits to the plotted data points. The horizontal axis depicts the number of connections remaining in tractography matrices. Only true positives were considered in thisanalysis.Thefinal10%ofvalueswereexcludedduetolowsamplesize.C,x-axisrepresentsfalsepositiverate(FPR);y-axisrepresentstruepositiverate(TPR).Resultssuggestsimilarperformance for pDT1 and pDT3. D, Sensitivity and specificity were similar for pDT1/3. Cutoff refers to the experimental connection weight detection threshold. therefore, pDT1 correlation was halved (r ϭ 0.28) when the between maximizing true positives and minimizing false posi- strongest 25% of connections had been removed. However, tives for this particular analysis. When thresholding from weakest modest correlation remains even for weak connections (after the to progressively stronger connections, the correlation coefficient strongest half of connections had been removed, pDT1: r Ͼ 0.2 remains relatively flat and is above r ϭ 0.5 at the threshold noted and pDT3: r Ͼ 0.1). here. To assess tractography’s ability to detect connections in a purely binary fashion, we performed a ROC analysis on the same Relationship between tractography accuracy and interareal data (Fig. 4C). This analysis produces a metric, the area under the path length curve (AUC), that quantifies the classifier’s accuracy (1 signifies We estimated interareal path lengths based on the streamline perfect prediction of tracer; 0.5 signifies no better than chance). trajectories generated by probabilistic tractography (see Materi- The AUC was 0.71 for pDT1 and 0.72 for pDT3, suggesting that als and Methods). These estimates are likely more accurate than tractography is a fair but far from perfect predictor of connection the piecewise-linear trajectories within WM used previously to presence. Sensitivity and specificity (Fig. 4D) also exhibit similar estimate interareal distances (Ercsey-Ravasz et al., 2013) because performance for pDT1 and pDT3. At a cutoff threshold of zero, observed anatomical trajectories can be curved or irregular sensitivity is almost unity (all but a few percent of tracer-based (Schmahmann and Pandya, 2009; Jbabdi et al., 2013) as they pathways are detected by unthresholded tractography), but spec- navigate around subcortical nuclei (e.g., basal ganglia, thalamus). ificity is about 0.1 (tractography correctly predicted only ϳ10% The pDT1/3-derived path lengths were highly correlated with of true negatives). The intersection of the sensitivity and specific- those reported by the tracer study (r ϭ 0.84; ␩2 ϭ 0.71). ity curves occurs at 0.65 for pDT1 and 0.67 for pDT3 (a value of 1 Correct classifications, false positives, and false negatives were being a perfect test). The associated cutoff value (6.5E-5 FSe for sorted by path length (Fig. 5A, 10 mm bins). False positives and pDT1 and 1.1E-4 FSe for pDT3) offers a balanced compromise false negatives were absent for path lengths Ͻ20 mm and their 6766 • J. Neurosci., June 22, 2016 • 36(25):6758–6770 Donahue et al. • Connection Strength and Distance with Tractography

Figure 5. Tractography performance as a function of path length. A, Number of correct tractography detections, false positives, and false negatives (using tracer as ground truth). B, Median connection weights of correctly classified connections binned by tractography-measured connection path length. C, Tracer connection weights versus tractography-derived path length. D, Tractography connection weights versus tractography-derived path length. Solid lines correspond to least absolute residual fit to data excluding points along axes. incidence increased with longer path lengths. Nevertheless, trac- tionship for tracers and extends it to tractography, in both cases tography performed reasonably well in identifying long connec- using the aforementioned tractography-derived path lengths as tions (up to 60–70 mm). Median values were determined for opposed to linear piecewise path length estimates computed in both tracer and tractography within each bin (Fig. 5B) and the tracer study (Markov et al., 2014). We used the slope (S)of showed that tractography correlated well with median tracer val- this line along with path length (PL) to regress the relationship ء Ͻ ϭ ϩ ues at path lengths 50 mm, but their values diverged at longer out of the data as follows: GDR G S PL. The result (Fig. path lengths. It is unsurprising that tractography is a stronger 6A) shows that the correlation between tractography and replace predictor of connection classification and characterization for is markedly reduced (r ϭ 0.22, ␩2 ϭ 0.05). shorter paths, but this analysis provides additional objective mea- We applied our previous correlation analysis that involved sures of performance as a function of connection path length. progressive removal of connections strongest to weakest (Fig. 4B) The relationship between a connection’s logarithmic weight after regressing out the estimated exponential path length rela- and its path length shows a quasilinear decline for both tracers tionship (Fig. 6B). This reduced the correlation over the whole (Fig. 5C) and tractography (Fig. 5D). This confirms a previously range of remaining connections relative to that shown in Figure reported (Ercsey-Ravasz et al., 2013) exponential distance rela- 4B, but, interestingly, the correlation remains positive even for Donahue et al. • Connection Strength and Distance with Tractography J. Neurosci., June 22, 2016 • 36(25):6758–6770 • 6767

Figure6. Comparisonoftracerversustractographylog-scaleconnectionweightswithreducedpathlengthdependency.A,Tracerandtractographylog-scaleconnectionweightsafterregression of estimated exponential relationship. Data points are depicted according to their corresponding path length bin (bin width ϭ 20 mm; excluded path lengths Ͼ80 mm, 2.5% of all connections). The solid line denotes the LAR fit to data excluding points along either. The dashed line ( y ϭ x) is for reference. B, Correlation between tractography and tracer connectivity weight in case PM1 for pDT1 and pDT3 after regression of estimated exponential relationship. Dotted lines represent second-order polynomial fits to the plotted data points. Data inclusion is as described in Figure 3. C, D, AnalysesfromAandBappliedtofull29ϫ91connectivitydataset.Theincreaseinfalsenegatives(nϭ128)andfalsepositives(nϭ788)wereproportionaltosamplesize.Thecorrelationbetween tracer and tractography connection weight was r ϭ 0.43. weak connections (right half of plot). We then expanded the their connection strength. Our analysis benefitted from a frac- analysis from the 29 ϫ 29 connectivity matrix to the full 29 ϫ 91 tional scaling normalization scheme to assess the correlation tracer and tractography matrices (Fig. 6C,D). Inclusion of these between connection weight metrics reported by these two mo- additional samples (unidirectional for tracer; bidirectional for dalities. We confirmed an exponential relationship between tractography) made the correlation curve less noisy and also connection weight and interareal path length and showed that strikingly flatter. Therefore, inclusion of unidirectional pathways tractography remains modestly predictive after regressing out degraded correlations for stronger pathways (left half of plot), this relationship. but strengthened the correlations when a much larger number of Of the two tractography seeding strategies used, the unidirec- weaker connections remain (right half). These observations sug- tional surface-to-surface method, producing dDT1, had a slight gest that tractography is modestly informative about anatomical performance advantage over the bidirectional voxel-to-surface connection weights over a wide range of connection weights and (dDT3) method. Relative to a geometrically predicted streamline path lengths beyond what can be surmised simply from their bias, dDT1 showed a bias similar in magnitude, but different in exponential relationship with distance. spatial pattern, whereas bias from dDT3 exceeded the predicted Discussion bias, especially in sulcal regions. When tracking out from the WM By comparing tractography-created cortical connectomes sys- (dDT3), streamline density tends to be lower in sulci and higher tematically with published parcellated connectome data de- in gyri (Van Essen et al., 2014). Our findings suggest that a strong rived from neuroanatomical tracers, we have shown that negative sulcal bias predominates over a weaker positive gyral current state-of-the-art tractography performs much better one. This is likely related to dense WM fiber bundles parallel to than chance, yet far from perfectly, in detecting neuroanat- the WM/GM boundary (Reveley et al., 2015), which (1) impede omical pathways and estimating weights corresponding to tractography detection of weaker crossing fiber bundles entering/ 6768 • J. Neurosci., June 22, 2016 • 36(25):6758–6770 Donahue et al. • Connection Strength and Distance with Tractography exiting GM in sulcal fundi and (2) include streamlines that run monkeys scanned), but the resulting tractography connectivity within these superficial WM bundles but fail to track accurately matrix was notably sparse (their Fig. 1B). We instead performed the relatively sparse fraction of axons within these bundles that separate analyses for correlating connectivity strength (using the branch or turn sharply to enter/exit the overlying GM. full connectivity matrix) and ROC analysis to describe the effects We found that tractography became less correlated with tracer of false positives and negatives. Finally, despite their low reported as strong connections were removed progressively. Importantly, correlation coefficients (accounting for Ͻ10% of observed vari- each weak interareal pathway involves far fewer neurons and ax- ance), they interpret their results more optimistically than we ons than each strong pathway. Therefore, in aggregate, weaker consider warranted for even our own data by stating that “in vivo pathways account for a small fraction of overall connectivity at DWI connectome reconstructions” “represent fairly realistic es- the level of cells and axons, though weak and strong pathways timates of the wiring strength of WM projections” and this is a both contributed to our reported correlation coefficients. “valid methodology for robust description and interpretation of Investigating tractography’s ability to classify connection ex- brain wiring” (van den Heuvel et al., 2015). istence using a ROC analysis revealed performance that can be Although our approach aimed to compare tractography with considered “fair” or “moderate” insofar as the AUC was 0.71 in tracers fairly, we also note limitations in the representation of the case of pDT1. In our data, the intersection of sensitivity and “ground truth” using retrograde tracers. First, repeated tracer specificity curves corresponded to a plausible tractography injections into the same portion of the same area vary approxi- threshold FSe of 6.5E-5 for pDT1 (1.1E-4 for pDT3). Although mately one order of magnitude around the group mean (Markov specific to this study, this threshold offers a starting point when et al., 2011), presumably reflecting a combination of genuine considering possible thresholds for other datasets, including hu- individual variability in connection weight, statistical fluctua- mans and other species in which connectivity “ground truth” is tions, and methodological limitations. Second, most identified completely lacking. connections are reciprocal but exhibit weight asymmetry (0.2 log The observed trend between connection weight and path length units on average). The incidence of nonreciprocal pathways re- in both tracer and tractography is consistent with previous observa- ported (Markov et al., 2014) exceeds that from an older meta- tions of a “noisy” exponential relationship (Ercsey-Ravasz et al., analysis (Felleman and Van Essen, 1991), but is comparable to 2013). Regressing out this relationship indicates that, whereas path recent studies in the mouse (Oh et al., 2014; Zingg et al., 2014), length is a major factor in estimating connection weights, tractogra- suggesting commonality of interareal pathway asymmetry. phy has useful explanatory power that transcends predictions based Third, we used a 91-area parcellation (Markov et al., 2014) based purely on connection path length. Algorithmic refinements that mainly on architectonic boundaries in a single atlas hemisphere. better model anatomically observed path length dependency may Methodological factors limit the fidelity with which the M132 enhance tractography’s utility in characterizing long-distance path- histology-based atlas parcellation was mapped to the individual ways (Liptrot et al., 2014). hemispheres used for tracer injections and to the Yerkes19 atlas. The quality of postmortem dMRI imaging data used here sur- Fourth, retrogradely labeled neuronal counts reflect only one as- passes typical spatial and angular resolutions used in conven- pect of connection weights. Anterograde tracers provide comple- tional in vivo dMRI, though recent advances such as multiband mentary information relating to axonal terminations, but results acceleration (Feinberg et al., 2010; Setsompop et al., 2012) can are harder to quantify accurately. Finally, there is substantial in- reduce this gap (Sotiropoulos et al., 2013). A previous analysis of ternal heterogeneity in the connectivity of a given area, especially different fiber orientation modeling methods (Thomas et al., those organized topographically (Markov et al., 2014). Because 2014) found that the original ball and stick model (Behrens et al., each retrograde tracer injection was restricted to one locus, ob- 2007) effectively balanced sensitivity and specificity when identi- served profiles of connection weights may inadequately represent fying connections and was robust to changes in angular thresh- the area as a whole. For tractography, this can be addressed by old. We used an improved ball and stick model that accounts for applying our “injection-site-to-area” method to additional sites. non-mono-exponential decay (Jbabdi et al., 2012), enabling esti- Our observations are relevant to human in vivo diffusion im- mation of up to three crossing fibers per voxel. By making these aging studies, including the high-resolution dMRI data from the datasets freely available, other investigators will be able to com- HCP (Sotiropoulos et al., 2013; Vu et al., 2015), but diverse dif- pare and contrast the performance of alternative fiber orientation ferences make such comparisons challenging. Human neocortex and tractography models. is ϳ10-fold larger than that of the macaque (Van Essen et al., A recent study (van den Heuvel et al., 2015) reported low 2012a, 2012b) and WM occupies a larger fraction of correlations (r ϭ 0.26–0.31) between macaque in vivo tractogra- volume. However, dMRI voxel sizes are larger (1.05 mm/1.25 phy and two macaque tracer datasets, the CoCoMac database mm for the HCP and conventionally 2 mm vs 0.43–0.5 mm in the and the Markov et al. (2014) dataset analyzed in the present present study), so the number of voxels spanning a gyral WM study. We attribute our twofold higher correlation (0.59) to dif- blade may be approximately comparable. Postmortem monkey ferences in analysis methods as well as data acquisition. For dMRI scans were longer (Ͼ60 h non-EPI, nonaccelerated postmortem acquisition, we used higher spatial resolution (0.43–0.5 vs 1.1 acquisitions vs 1 h for HCP and typically less for human in vivo mm isotropic voxels), angular resolution (120 vs 60 diffusion using EPI, often accelerated) and used higher b values, compen- directions), b values (8000 vs 1000 s/mm), and scan durations. sating for reduced diffusivity ex vivo compared with in vivo Higher spatial and angular resolution may improve the fidelity of (D’Arceuil et al., 2007). Given these anatomical and methodolog- tractography modestly (Sotiropoulos et al., 2013; Thomas et al., ical differences, the correlation between tractography-based con- 2014; Jbabdi et al., 2015; Wu and Zhang, 2016). Potentially im- nectivity and a hypothetical “ground truth” connectivity in portant analysis differences include our finer-grained parcella- humans might in principle be either higher or lower than what we tion (the 91-area Markov parcellation vs their 39 area “WBB47” reported here for monkeys. Our evidence that monkey tractog- parcellation). van den Heuvel et al. (2015) attempted to reduce raphy connection weight estimates are accurate to within one or effects associated with tractography false positives by threshold- two orders of magnitude relative to tracer-based ground truth ing based on reproducibility of connections (Ͼ60% of the 10 suggest that quantitative studies in humans may be limited to an Donahue et al. • Connection Strength and Distance with Tractography J. Neurosci., June 22, 2016 • 36(25):6758–6770 • 6769 approximately comparable degree using high-quality data such tical connectivity based on a distance rule. Neuron 80:184–197. 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